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- W4231717412 abstract "Let K be a compact set, $mathcal {M}$ a prescribed family of (possibly signed) Borel measures of total mass one supported by K, and f a continuous real-valued function on $K times K$. We study the problem of determining for which $mu in mathcal {M}$ (if any) the energy integral $I(K,mu ) = smallint _K {smallint _K {f(x,y)dmu (x)dmu (y)} }$ is maximal, and what this maximum is. The more symmetry K has, the more we can say; our results are best when K is a sphere. In particular, when $mathcal {M}$ is atomic we obtain good upper bounds for the sums of powers of all $(_2^n)$ distances determined by n points on the surface of a sphere. We make use of results from Schoenbergâs theory of metric embedding, and of techniques devised by Pólya and Szegö for the calculation of transfinite diameters." @default.
- W4231717412 created "2022-05-12" @default.
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- W4231717412 date "1974-06-01" @default.
- W4231717412 modified "2023-10-17" @default.
- W4231717412 title "Extremal Problems of Distance Geometry Related to Energy Integrals" @default.
- W4231717412 doi "https://doi.org/10.2307/1996898" @default.
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